The density of weakly complete problems under adaptive reductions

Given a real number /spl alpha/<1, every language that is weakly /spl les//sub n/spl alpha//2-T//sup P/-hard for E or weakly /spl les//sub n/spl alpha/-T//sup P/-hard for E/sub 2/ is shown to be exponentially dense. This simultaneously strengthens results of J.H. Lutz and E. Mayordomo (1994) and B. Fu (1995).